Lyn is correct, but I'd like to add something. 'Beating someone up' is when someone causes a lot of physical harm or stress to someone. They intend to not just shock someone with one or a few punches, but to go further by causing a lot more physical upset. Someone can beat someone up with repeated punches, using their fists or an object such as a slab of wood or a baseball bat, causing them to fall, break a bone, knock them out, or cause a lot of swelling and bleeding. A punch is just the fist hitting the other person.

Hello Alina! If I understand your question correctly; to "beat somebody" means to hit them repeatedly, with a fist or with an object that will inflict damage. to "punch somebody" means to hit them with a fist. I hope that helps!